The National Weather Service has issued a winter storm watch for much of Central, Northern, and Eastern Massachusetts, including the Boston area, saying a weekend storm could dump 3 to to 7 inches of heavy, wet snow.

In higher terrain areas, the forecasters said, 6 to 10 inches could fall.

The forecasters said the weight of the snow could bring down tree limbs and cause scattered power outages. They also warned that untreated roads could become snow-covered and slippery.

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A snowfall forecast map issued by the weather service this afternoon showed 2 to 4 inches falling along the coast in Boston, with 4 to 6 inches falling in the western suburbs. The snowfall amounts taper off to the south and east and increase to the north and west. A swath in northern Central Massachusetts could get up to 10 inches, according to the map.

Snow is expected to overspread the region Saturday afternoon and intensify Saturday night into Sunday morning.

Forecasters said it was possible that the snow would mix with rain near and just south of the Massachusetts Turnpike, then turn back into snow early Sunday morning before tapering off.

Forecasters said they were dealing with a “tricky forecast” because of uncertainty about the track of a storm passing along the coast and temperatures, which will determine whether the storm’s precipitation would fall as rain or snow. They noted that the supercomputer models used to predict the weather had been “flipflopping.”

In the afternoon forecast, they lowered the expected totals from their predictions this morning.

In a discussion posted on the Web, forecasters also warned of the possibility of minor coastal flooding and beach erosion.